I think so, besides, what we do know as well as also perhaps Naruto and Karin's being effectively cousins and all that.
Here's a drawing I did of Naruto and Sakura's son, Jiraiya (8 years old). His eyes are meant to be green like his mom's, and his hair being red is part of his Uzumaki heritage as well as a combo of his mom and dad's hair colors, kind of like how Naruto's moniker of the Orange Hokage is a mix of Minato's of the Yellow Flash and Kushina's of the Red-Hot Habanero.
Indeedy. There's plenty of story that could be explored there.
Nice What kind of personality does this Jiraiya have?